Dynamic behavior of nonlinear Goodwin oscillator based on data-driven modeling

Abstract

Recent advancements in economic dynamics have been significantly shaped by the development of the Goodwin model and the application of nonlinear dynamics theory to economic systems. This study extends the classical Goodwin model by incorporating an empirically derived investment function to more precisely characterize investment dynamics within real economic systems. Furthermore, economic systems are frequently subject to exogenous shocks, leading to substantial market fluctuations that traditional deterministic models often fail to adequately capture. To address this limitation, this study employs a Goodwin model driven by Lévy noise to represent the stochastic evolution of economic systems. An analysis of the data-driven Goodwin model subject to Lévy noise excitation indicates that parameter variations significantly influence the steady-state probability density distribution, particularly affecting peak adjustments, which in turn impact income levels. This study underscores the pivotal role of parameter adjustments in economic modeling, particularly in relation to system dynamics and the mean first passage time (MFPT). The findings demonstrate that both additive and multiplicative Lévy noise expedite state transitions between stabilization points, thereby facilitating shifts between different equilibrium states. However, this transition acceleration is accompanied by an increase in income level fluctuations. Additionally, the results suggest that excessive government intervention in economic parameters may constrain income volatility, whereas targeted parameter adjustments can modulate transition rates and contribute to noise-induced stabilization.